Deterministic lateral displacement arrays

ABSTRACT

A deterministic lateral displacement array that includes a channel, within a substrate, having a first sidewall, a second sidewall, and a channel length. A condenser portion that includes an entry port and an exit port. A first array of pillars is disposed between the entry port and the exit port of the condenser portion along the channel length, the first array of pillars operative to drive a first material particle and a second material particle towards the first sidewall of the channel. A separator portion that includes an entry port and an exit port, and a second array of pillars disposed between the entry port and the exit port of the separator portion along the channel length, the pillars operative to drive the first material particle towards the second sidewall of the channel.

This application is a divisional of Non-Provisional application Ser. No.15/270,514, filed Sep. 20, 2016, the disclosure of which is incorporatedby reference herein in its entirety.

BACKGROUND

The present invention relates in general to deterministic lateraldisplacement arrays and, more specifically, to using deterministiclateral displacement arrays for particle separation.

In microfluidic devices, the fluid behaves according to the laws oflaminar flow, which has high viscosity and no inertia motion. Due to thelack of inertia motion, the flow has time reversibility that makes themixing of two parallel flow streams challenging on a practicaltimescale. Adjacent flow streams can be used to compress and “sculpt” aliquid stream without diluting the contents (e.g. particles, analytes)of the stream itself. This method is called hydrodynamic focusing andhas been used to generate concentrated “jets” of fluid flow, with narrowcross-sections, for microfluidic applications such as emulsion formationand localized sample feeding. This method has the ability to concentratea stream of fluid or sample, thus reducing diffusion effects, increasingthe local density of analytes, and allowing controlled spatial placementof the stream within a fluidic channel.

SUMMARY

According to an embodiment of the present invention, a method of forminga deterministic lateral displacement array is provided. The methodincludes forming a channel, within a substrate, having a first sidewall,a second sidewall, and a channel length. The channel includes acondenser portion and a separator portion. The condenser portionincludes an entry port and an exit port. The method includes forming afirst array of pillars disposed between the entry port and the exit portof the condenser portion along the channel length, the first array ofpillars operative to drive a first material particle and a secondmaterial particle towards the first sidewall of the channel and theseparator portion includes an entry port and exit port, the entry portof the separator portion arranged with the exit portion of the condenserportion such that the first material particle and the second materialparticle flow from the exit port of the condenser portion into the entryport of the separator portion. Forming a second array of pillarsdisposed between the entry port and the exit port of the separatorportion along the channel length, the pillars operative to drive thefirst material particle towards the second sidewall of the channel.

According another embodiment of the present invention, a deterministiclateral displacement array is provided. The deterministic lateraldisplacement array includes a channel, within a substrate, having afirst sidewall, a second sidewall, and a channel length. A condenserportion that includes an entry port and an exit port. A first array ofpillars disposed between the entry port and the exit port of thecondenser portion along the channel length, the first array of pillarsoperative to drive a first material particle and a second materialparticle towards the first sidewall of the channel. A separator portionthat includes an entry port and an exit port, the entry port of theseparator portion arranged with the exit port of the condenser portionsuch that the first material particle and the second material particleflow from the exit port of the condenser portion into the entry port ofthe separator portion and a second array of pillars disposed between theentry port and the exit port of the separator portion along the channellength, the pillars operative to drive the first material particletowards the second sidewall of the channel.

According to another embodiment of the present invention, a method forforming a deterministic lateral displacement array is provided. Themethod includes forming a channel, within a substrate, having a firstsidewall, a second sidewall, and a channel length. The channel includesa condenser portion and a separator portion. The condenser portionincludes an entry port and an exit port. The method includes forming afirst array of pillars disposed between the entry port and the exit portof the condenser portion along the channel length, the first array ofpillars operative to drive a first material particle and a secondmaterial particle towards a center of the channel equidistance from thefirst sidewall and the second sidewall and the separator portionincludes an entry port and exit port, the entry port of the separatorportion arranged with the exit portion of the condenser portion suchthat the first material particle and the second material particle flowfrom the exit port of the condenser portion into the entry port of theseparator portion. Forming a second array of pillars disposed betweenthe entry port and the exit port of the separator portion along thechannel length, the pillars operative to drive the first materialparticle towards both the first sidewall and the second sidewall.

According to anther embodiment of the present invention, a deterministiclateral displacement array is provided. The deterministic lateraldisplacement array includes a channel, within a substrate, having afirst sidewall, a second sidewall, and a channel length. A condenserportion that includes an entry port and an exit port. A first array ofpillars disposed between the entry port and the exit port of thecondenser portion along the channel length, the first array of pillarsoperative to drive a first material particle and a second materialparticle towards a center of the channel equidistance from the firstsidewall and the second sidewall. A separator portion that includes anentry port and an exit port, the entry port of the separator portionarranged with the exit port of the condenser portion such that the firstmaterial particle and the second material particle flow from the exitport of the condenser portion into the entry port of the separatorportion and a second array of pillars disposed between the entry portand the exit port of the separator portion along the channel length, thepillars operative to drive the first material particle towards both thefirst sidewall and the second sidewall.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter of the present invention is particularly pointed outand distinctly defined in the claims at the conclusion of thespecification. The foregoing and other features and advantages areapparent from the following detailed description taken in conjunctionwith the accompanying drawings in which:

FIG. 1 illustrates a top down partially cut-away view of a deterministiclateral displacement array;

FIG. 2 illustrates a top down view of a first portion of thedeterministic lateral displacement array;

FIG. 3 illustrates a top down view of a portion of the array of fourpillars in a condenser that includes four pillars;

FIG. 4 illustrates a cross-sectional view, along the line X-X′ of FIG.2;

FIG. 5 illustrates a top down view of an example of second portion ofthe deterministic lateral displacement array;

FIG. 6 illustrates a top down view of a portion of the array of pillarsin a separator that includes four pillars;

FIG. 7 illustrates a graph showing the predicted migration angle of aparticle in an array with pillar diameter and pillar center distancethat is substantially perpendicular to the flow direction;

FIG. 8 illustrates a top down partially cut-away view of an alternativeexemplary embodiment of a deterministic lateral displacement array; and

FIG. 9 illustrates a top down partially cut-away view of a particlecondenser according to one or more embodiments of the present invention.

DETAILED DESCRIPTION

Deterministic lateral displacement (DLD) devices are utilized toseparate particles within a fluid. The embodiments described hereinfocus particle concentrations within a channel and then separate largerparticles from smaller particles. Microfluidic devices often utilizehydrodynamic focusing to generate a concentrated jet of fluid flow.However, the focusing jet uses extra channels with specific pressurecontrols. The focusing jets involve additional complexity for tuning andcareful control on the focusing process. The embodiments describedherein focus particles within a fluid flow without extra side channelsor electric fields.

A deterministic lateral displacement arrays is provided. Embodimentsdescribed herein include a channel within a substrate that contains acondenser portion and a separator portion. The channel length in boththe condenser and separator portions has a first and second sidewall. Inthe condenser portion, there is an entry and exit port that receives afluid containing two particles, a large particle and a small particle.Within the channel of the condenser portion is a first array of pillarsthat are disposed between the entry and exit port along the length ofthe channel. The arrangement of the first array of pillars in thecondenser portion drives both the large particles and the smallparticles towards the first sidewall of the condenser portion. In theseparator portion, there is an entry and exit port capable of receivingthe fluid. Within the channel of the separator portion is a second arrayof pillars that are disposed between the entry and exit port along thelength of the channel within the separator. The arrangement of thesecond array of pillars in the separator portion drives the largeparticle towards the second side wall of the separator portion.

FIG. 1 illustrates a top down partially cut-away view of an exemplaryembodiment of a deterministic lateral displacement array. Thedeterministic lateral displacement array 100 includes a condenserportion (condenser) 102 and a separator portion (separator) 104. Each ofthe condenser 102 and separator 104 includes a channel 106. Disposedwithin the channel 106 are a first patterned array 203 (of FIG. 2) ofpillars 204 (of FIG. 2) and a second patterned array 503 (of FIG. 5) ofpillars 504 (of FIG. 5). Each of the condenser 102 and separator 104includes a first sidewall 108 and a second sidewall 110. The condenser102 includes an entry port 118 and an exit port 120. The separator 104includes an entry port 122, which abuts to the exit port 120 of thecondenser, and an exit port 124.

The deterministic lateral displacement array 100 is operative to receivea fluid. In the illustrative example, the fluid includes a firstmaterial 112 and a second material 114 that are suspended in the fluid.The first material 112 has a first particle size and the second material114 has a second particle size. In the illustrated exemplary embodiment,the first particle size is larger than the second particle size. Whilethe illustrative example shows a fluid with two materials, any number ofmaterials within a fluid can be passed into the deterministic lateraldisplacement array 100. The flow direction 116 of the fluid is shown tobe substantially axial along the length of the channel.

In operation, the condenser 102 first concentrates the first and secondparticles of the first 112 and second 114 material into a focused jetclose to the first sidewall 108. The separator 104 then separates thelarger particles from the smaller particles by forcing the largerparticles of the first material 112 towards the second sidewall 110. Thesmaller particles of the second material 114 generally follow the fluidflow direction 116.

FIG. 2 illustrates top down view of the first portion of thedeterministic lateral displacement array according to one or moreembodiments. The first portion of the deterministic lateral displacementarray is the condenser 102. The condenser 102 includes a channel 106, afirst sidewall 108 and second sidewall 110. Disposed within the channel106, is an array 203 of pillars 204. The condenser 102 includes an inputport 118 and an output port 120.

The pillars 204 are disposed on the channel 106 and arranged in apatterned array 203. The array 203 of pillars 204 are arranged orpatterned with a desired size, shape, and relative position toconcentrate the large particles at the first sidewall 108. The largeparticles have an over-critical diameter, as it relates to the array203, and migrate towards the first sidewall 108. When the largeparticles traverse the condenser 102, the large particles bump throughthe off-shifted pillars 204 and migrate along a bumping direction 210.The smaller particles do not have an over-critical diameter, and, thus,migrate in a zig-zag shaped path 212 along the pillar array 203.

FIG. 3 illustrates a top down view of a portion of the array 203 ofpillars 204 in the condenser 102 that includes four pillars 202. Theother pillars in the array 203 in the condenser 102 are sized and shapedin a similar arrangement as the four pillars 202. The four pillars 202include the following geometric parameters: a D₀, a D_(y), a D_(x), a G,and a Δ. The D₀ is a diameter of a pillar 204. The D_(x) is the centerto center distance between pillar centers substantially parallel to theflow direction 116. The D_(y) is the center to center distance betweenpillar centers substantially perpendicular to the flow direction 116.The G is a gap distance between pillars, which is the distance betweenthe outer surfaces of two pillars. And the Δ is the off-set displacementof a pillar with respect to another pillar in the flow direction 116.The four pillars 202 illustrate a portion of the array of pillars. Inone or more embodiments, the geometric parameters of the four pillars202 are uniform across the array of pillars within the condenser 102. Inone or more embodiments, the pillars 204 in the array 203 can follow asimilar size, shape, and arrangement as the four pillars 202 within thecondenser 102.

FIG. 4 illustrates a cross-sectional view along the line X-X′ of FIG. 2according to the illustrated exemplary embodiment. The cross-sectionalview includes a floor 402, a cover 404, the first sidewall 108, and thesecond sidewall 110 of the deterministic lateral displacement array 100.Disposed on the lower wall 402 are the pillars 204 with the geometricparameters of D₀ and G. D₀ is the diameter of each of the pillars 204and G is the gap distance between the outer surfaces of the pillarssubstantially perpendicular to the flow direction 116. D_(y) is thecenter to center distance between pillar centers substantiallyperpendicular to the flow direction 116. The pillars 204 are shownwithin the channel 106. The cover 404 is not shown in FIG. 2.

FIG. 5 illustrates a top down view of an example of the second portionof the deterministic lateral displacement array. The second portion ofthe deterministic lateral displacement array is the separator 104. Theseparator 104 includes a channel 106, a first sidewall 108, and secondsidewall 110. Disposed within the channel 106, is an array 503 ofpillars 504. The separator 104 includes an input port 122 and an outputport 124.

The pillars 504 are disposed on the channel 106 and arranged in apatterned array 503. The pillars 504 are arranged or patterned with adesired size, shape, and relative position to concentrate the largeparticles at the second sidewall 110. The large particles have anover-critical diameter. Because the large particles have the larger orover-critical diameter, when fed through the condenser 102, the largeparticles bump through the off-shifted pillars 504 and migrate along abumping direction 510 towards the second sidewall 110. The smallerparticles do not have an over-critical diameter, and, thus, migrate in azig-zag shaped direction 512 along the pillar array 503. Due to thegeometric parameters of the separator, the smaller particles generallyfollow the fluid flow direction 116.

FIG. 6 illustrates a top down view of a portion of the array 503 ofpillars 504 in the separator 104 that includes four pillars 502. Thefour pillars 502 include the following geometric parameters: a D₀′, aD_(y)′, a D_(x)′, a G′, and a Δ′. The pillars 204 in the condenser 102have geometric parameters that can be different from the geometricparameters of the pillars 504 in the separator 104. The D′₀ is adiameter of a pillar 504. The D_(x)′ is the center to center distancebetween pillar centers substantially parallel to the flow direction 116.The D_(y)′ is the center to center distance between pillar centerssubstantially perpendicular to the flow direction 116. The G′ is a gapdistance between pillars, which is the distance between the outersurfaces of two pillars. And the Δ′ is the off-set displacement of apillar with respect to another pillar in the flow direction 116. Δ′ canbe referred to as the row-shift displacement. The four pillars 502illustrate a portion of the array 503 of pillars 504. In one or moreembodiments, the four pillars 502 follow a similar size, shape, andarrangement as the array 503 of pillars 504 within the separator 104.

The condenser 102 is utilized for focusing the larger and smallerparticles with a maximum asymmetric penetrability. The separator 104 isutilized for separating the particles by the size difference with anincreased migration angle difference. The pillars 204, 504 within thepillar array 203, 503 are constructed within a fluidic channel 106 inwhich a fluid flow follows axially along the direction of the channel(i.e. the flow direction 116), while a lattice translation vectorfollows along at an angle set by the geometric parameters of the pillars204, 504 within the pillar array 203, 503. This angle is referred to asthe bumping angle. Should a particle be deflected by the array, theangle of the particle follows the bumping angle. If the particle isdeflected by less than the bumping angle, it can be referred to as themigration angle. If a particle follows the flow stream in the channel106, then its motion is called a zig-zag mode and its migration angle iseffectively zero.

FIG. 7 illustrates a graph 700 showing the predicted migration angle ofa particle in an array with pillar diameter (D₀) and pillar centerdistance (D_(y)) which is perpendicular to the flow direction 116. Thex-axis shows the ratio of pillar diameter (D₀) to pillar center distance(D_(y)), i.e., D₀/D_(y). This ratio can also be referred to as themigration ratio. The y-axis shows the degree, W, by which two particlesdiverge. The two particles are referred to as the large particle andsmall particle. θ_(p) is the migration angle of the bumping particle(i.e. the large particle). θ is the migration angle of the zig-zagparticle (i.e. the small particle).

N is the row shift ratio which shows the ratio of the pillar centerdistance (D_(y)) to the row-shift displacement (Δ), i.e. D_(y)/Δ. In theillustrative example, the row shift ratios are N=5 and N=10. The graphline for N=5 is shown as 602 and the graph line for N=10 is shown as604. As the D₀/D_(y) ratio tends towards one, the ratio between the twomigration angles (θ and θ_(p)) tends to one. As the D₀/D_(y) ratio tendsto one, the migration angles are close and the two particles are movingat the similar angle as seen in the condenser 104. In one or moreembodiments, for a condenser 102, the D₀/D_(y) is in the range of0.6-0.7 and for a separator 104, the D₀/D_(y) is in the range of0.3-0.4. The separator 104 has a lower ratio of migration angles becauseit is diverting the particles away from the narrow particle streamcreated by the condenser 102. By changing the geometric parameters inthe pillar array, the zig-zag motion of the smaller particle can bechanged from a zero value to a non-zero value thus diverting theparticle out of the normal flow stream of the fluid.

In the exemplary case of N=5, the result of graph 700 can be fitted withthe function y=1.2116×{circumflex over ( )}2.0748 and in the case ofN=10, the results of graph 700 can be fitted with the functiony=1.2068×{circumflex over ( )}1.7508. Therefore, once the ratio D₀/D_(y)is determined, the migration ratio between the large particle and thesmall particle is determined. After the migration ratio is determined, amigration angle for the small particles is calculated.

The geometric parameters of the pillars 204 in the array 203 in thecondenser 102 can be calculated according to the following example.Assuming the large particle diameter is 500 nm and the small particle is300 nm and N=5 in the array 203, the calculated target diameter, D_(c),is 400 nm. D_(c) is determined utilizing the formulaD_(c)=1.4G(1/N){circumflex over ( )}0.48. From this formula, the gap Gis determined to be 870 nm.

In condenser 102, a D₀/D_(y) ratio is chosen between 0.6-0.7 to make themigration angle of large and small particles close to each other. In theexample, if 0.6 is choses as the value for the D₀/D_(y) ratio and G=870nm, utilizing the formula (D_(y)=D₀+G), the calculated values for thefollowing parameters are D_(y)=1550 nm and D₀=930 nm. From thesecalculated values, the migration angles can be calculated utilizing afitting function. The bumping angle is ARCTAN (1/N)=11.31 degrees andthe migration ratio is 0.42 from the fitting function(y=1.2116×{circumflex over ( )}2.0748). The migration angle of the smallparticle is 4.75 degrees. With a channel that is 50 μm wide and 600 μmlong, the particles are focused as desired.

In the illustrative example, the graph 700 shows that as the ratiobetween the pillar diameter and the center to center distance of thepillars, the asymmetric permeability increases. The flow is focused moretoward the first sidewall 108 of the channel as propagating along thepressure gradient direction (i.e. the flow direction 116). The focusingis controlled by the geometric parameters of the pillar array and theoff-shift displacement (N).

FIG. 8 illustrates a top down view of an alternate exemplary embodimentof a deterministic lateral displacement array. The deterministic lateraldisplacement array 800 includes a condenser 802 and a separator 804.Each of the condenser 802 and separator 804 includes a channel 806. Eachof the condenser 802 and separator 804 includes a first sidewall 808 anda second sidewall 810. The condenser 802 includes an entry port 818 andan exit port 820. The separator 804 includes an entry port 822, whichabuts to the exit port 820 of the condenser, and an exit port 824.

Within the channel 806 are a first and second patterned array of pillarsthat are similar to the first and second patterned array of pillars inFIG. 2 and FIG. 5. The pillars in the array of the condenser 802 havegeometric parameters as described above in FIG. 3 and FIG. 6. Thepillars in the array have a desired size, shape, and relative positionthat concentrate the large particles and the small particles to thecenter of the channel 806 roughly equidistance between the first 808 andsecond 810 sidewalls. The pillars in array of the separator havegeometric parameters as described above in FIG. 3 and FIG. 6. Thepillars in the array have a size, shape, and relative position thatconcentrate the larger particles of the first material 812 to each ofthe first sidewall 808 and the second sidewall 810. The size, shape, andrelative position of the pillars in the array cause the smallerparticles to generally follow the fluid flow path 816.

The deterministic lateral displacement array 800 is operative to receivea fluid. In the illustrative example, the fluid includes a firstmaterial 812 and a second material 814. The first material 812 hasparticles of a first particle size and the second material 814 hasparticles of a second particle size. The first particle size is largerthan the second particle size. While the illustrative example shows afluid with two materials, any number of materials within a fluid can bepassed into the deterministic lateral displacement array 800. The flowdirection 816 of the fluid is shown to be axial along the direction ofthe channel 806.

The condenser 802 first concentrates the first and second particles ofthe first 812 and second 814 material into a focused jet close to thecenter of the channel 806 roughly equidistance between the first 808 andsecond 810 sidewalls. The separator 804 then separates out the largerparticles by forcing the larger particles of the first material 812 toeach of the first sidewall 808 and the second sidewall 810. The smallerparticles of the second material 814 are not forced to either of thesidewalls.

FIG. 9 illustrates a top down view of an exemplary embodiment of aparticle condenser. The particle condenser 900 includes a firstcondenser 902 and a second condenser 904. Each of the first condenser902 and the second condenser 904 includes a channel 906. Within thechannel 906 are a first and a second patterned array of pillars whichare similar to the first patterned array 203 of FIG. 2. Each of thefirst condenser 902 and the second condenser 904 includes a firstsidewall 908 and a second sidewall 910. The first condenser 902 includesan entry port 918 and an exit port 920. The second condenser 904includes an entry port 922, which abuts to the exit port 920 of thefirst condenser 902, and an exit port 924.

The particle condenser 900 is operative to receive a fluid. In theillustrative example, the fluid includes a first material 912 and asecond material 914. The first material 912 has a first particle sizeand the second material 914 has a second particle size. In one or moreembodiments, the first particle size is larger than the second particlesize. While the illustrative example shows a fluid with two materials,more than two materials within a fluid can be passed into the particlecondenser 900. The flow direction 916 of the fluid is shown to be axialalong the direction of the channel 906.

The first condenser 902 first concentrates the first and secondparticles of the first 912 and second 914 material into a focused jetclose to the first sidewall 908. The second condenser 904 then focusesthe first particles of the first material 912 as well as the secondparticles of the second material 914 to even closer to the firstsidewall 908. In one or more embodiment, a separator can be placed atthe exit port 924 of this first 902 and second 904 condensercombination.

The deterministic lateral displacement arrays 100, 800, and the particlecondenser 900 can be constructed on silicon wafers, patterned by, forexample, photolithographic patterning and etching processes. In theillustrated example, features such as pillars are etched by using anetching process to obtain nearly vertical sidewalls. Devices can becoated with a fluorosilicate vapor and sealed by glass coverslips coatedwith polydimethylsiloxane (PDMS) silicone on the sealing surface. Thedeterministic lateral displacement arrays 100, 800, and the particlecondenser 900 can be placed into a Plexiglas chuck for loading andapplication of pressures.

The deterministic lateral displacement arrays 100, 800, and particlecondenser 900 can be micro/Nano-fabricated. Microfabrication techniquescan be selected from, for example, techniques conventionally used forsilicon-based integrated circuit fabrication, embossing, casting,injection molding, and so on. Examples of suitable fabricationtechniques include photolithography, electron beam lithography, imprintlithography, reactive ion etching, wet etch, laser ablation, embossing,casting, injection molding, and other techniques. The deterministiclateral displacement arrays 100, 800, and particle condenser 900 can befabricated from materials that are compatible with the conditionspresent in the particular application of interest. Such conditionsinclude, but are not limited to, pH, temperature, application of organicsolvents, ionic strength, pressure, application of electric fields,surface charge, sticking properties, surface treatment, surfacefunctionalization, and bio-compatibility. The materials of the deviceare also chosen for their optical properties, mechanical properties, andfor their inertness to components of the application to be carried outin the device. Such materials include, but are not limited to, glass,fused silica, silicone rubber, silicon, ceramics, and polymericsubstrates, e.g., plastics, depending on the intended application.

Technical benefits include the asymmetric flow profile due to the pillararrays. The geometry of the pillar array (e.g. pitch, pillar size,lattice constants) determines to what extent a pillar array will be ableto separate larger particles from smaller particles. Tuning thegeometric parameters of the array allows a designed arrays that eithercan separate larger particles from smaller particles (these arrays aretermed separators), or which distort all particle paths by causing anasymmetric flow, causing all particles to be pushed to one side of thearray. These later arrays are termed condensers, as they have the effectto displace all particles and concentrate them on one side of a pillararray channel. Condensers can be used to focus particles into a narrowjet without the use of additional flow streams or pressure control, thussimplifying the design of fluidic systems. Concentration of particlesallows (1) reducing the effects of diffusion, (2) formation of narrowjets which can then be fed into separators to achieve high resolutionparticle fractionation, all in a single channel, and (3) increases theconcentration of a sample, which can be useful for rare or highlydiluted particle solutions needed in a diagnostic. In one or moreembodiments, the invention encompasses the idea of using different setsof arrays with different geometric parameters, in sequence or parallel,to generate “lensing” effects on particle streams, opening thepossibility for manipulating particle flows by manipulating thestructures through which the flows pass.

Additional technical benefits include utilizing a two stage approachthat is advantageous because the separation efficiency depends on thecross-section of the particle jet. Diffusion ultimately limits theresolution of a separator array; the more narrow a particle jet injectedinto a separator, the more time (spatial extend) is available toseparate the particle streams. By tuning the condenser, narrow particlejets can be made such that there is no overlap between the bumped (largeparticle) and zig zag mode (small particle) jets in the separatordevice, leading to high resolution and optimum performance. Usingcondenser geometry simplifies this jet formation process, allowing asmaller device footprint and thus larger scale integration (higherdevice density). The condenser has flexibility in terms of where theconcentration can be formed; narrow jets can be focused to any positionalong the width of the channel by having two sets of pillar arrays,parallel to each other, with varied bumping directions.

Additional technical benefits include the combined effect of focusing anentire particle flux to the rights side of the array of pillars,effectively concentrating the first and second material to a narrowvolume. The advantage to this is the ability to concentrate particles ofall sizes into narrow stream of jet without having to use any additionalinput fluid or pressure. Current methods require stream focusing togenerate this narrow stream which includes a concentrated particle jetwhich requires at least one or two additional input flows which requirebalancing of the pressures between the particle flow and the inputflows. Therein lays a difficulty of scaling and controlling thesemultiple flows, especially for large scale, parallel device integration.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

What is claimed is:
 1. A method for forming a deterministic lateraldisplacement array, the method comprising: forming a channel, within asubstrate, having a first sidewall, a second sidewall, and a channellength; the channel includes a condenser portion and a separatorportion; the condenser portion includes an entry port and an exit port;forming a first array of pillars disposed between the entry port and theexit port of the condenser portion along the channel length, the firstarray of pillars operative to drive a first material particle and asecond material particle towards a center of the channel substantiallyequidistance from the first sidewall and the second sidewall; and theseparator portion includes an entry port and exit port, the entry portof the separator portion arranged with the exit portion of the condenserportion such that the first material particle and the second materialparticle flow from the exit port of the condenser portion into the entryport of the separator portion; and forming a second array of pillarsdisposed between the entry port and the exit port of the separatorportion along the channel length, the pillars operative to drive thefirst material particle towards both the first sidewall and the secondsidewall.
 2. The method of claim 1, wherein the first material particlehas a first particle size.
 3. The method of claim 2, wherein the secondmaterial particle has a second particle size.
 4. The method of claim 3,wherein the first particle size is greater than the second materialparticle size.
 5. The method of claim 1, wherein the first array ofpillars comprises: a first pair of pillars and a second pair of pillars;the first pair of pillars comprises a first pillar and a second pillar;and the second pair of pillars comprises a third pillar and a fourthpillar.
 6. The method of claim 5, wherein: the first pillar and thesecond pillar have a first diameter of D₀ length; the first pillar has acentral axis and the second pillar has a central axis, the central axisof the first pillar and the central axis of the second pillar define afirst line having a length D_(y) that is substantially perpendicular tothe first sidewall.
 7. The method of claim 6, wherein: the third pillarand the fourth pillar have a first diameter of D₀ length; the thirdpillar has a central axis and the fourth pillar has a central axis, thecentral axis of the third pillar and the central axis of the fourthpillar define a second line having a length D_(y) that is substantiallyperpendicular to the first sidewall.
 8. The method of claim 7, whereinthe central axis of the first pillar and the central axis of the thirdpillar are off-set by Δ distance in an off-set direction, the off-setdirection is substantially perpendicular to the first sidewall.
 9. Themethod of claim 8, wherein the central axis of the second pillar and thecentral axis of the fourth pillar are off-set by Δ distance in theoff-set direction.
 10. The method of claim 1, wherein the second arrayof pillars comprises: a third pair of pillars and a fourth pair ofpillars; the third pair of pillars comprises a fifth pillar and a sixthpillar; and the fourth pair of pillars comprises a seventh pillar and aneighth pillar.
 11. The method of claim 10, wherein: the fourth pillarand the fifth pillar have a second diameter of D₀′ length; and the fifthpillar has a central axis and the sixth pillar has a central axis, thecentral axis of the fifth pillar and the central axis of the sixthpillar define a third line having a length D_(y′) that is substantiallyperpendicular to the first sidewall.
 12. The method of claim 11,wherein: the sixth pillar and the seventh pillar have a second diameterof D₀′ length; the seventh pillar has a central axis and the eighthpillar has a central axis, the central axis of the seventh pillar andthe central axis of the eighth pillar define a fourth line having alength D_(y)′ that is substantially perpendicular to the first sidewall.13. The method of claim 12, wherein the central axis of the fifth pillarand the central axis of the seventh pillar are off-set by Δ′ distance inan off-set direction, the off-set direction is substantiallyperpendicular to the first sidewall.
 14. The method of claim 13, whereinthe central axis of the sixth pillar and the central axis of the eighthpillar are off-set by Δ′ distance in the off-set direction.
 15. Themethod of claim 9, wherein the first material particle has a migrationangle of θ_(p) in the condenser portion; the second material particlehas a migration angle of θ in the condenser portion; wherein a degree ofdivergence of the first material particle and the second materialparticle in the condenser portion is defined by θ/θ_(p); and the degreeof divergence is a function of D₀/D_(y).
 16. The method of claim 15,wherein the condenser portion includes a degree of divergence that tendsto one as D₀/D_(y) tends to one.
 17. The method of claim 13, wherein thefirst material particle has a migration angle of θ_(p) in the condenserportion; the second material particle has a migration angle of θ in theseparator portion; wherein a degree of divergence of the first materialparticle and the second material particle in the separator portion isdefined by θ/θ_(p); and the degree of divergence is a function ofD₀/D_(y).
 18. The method of claim 15, wherein a degree of divergence ofthe condenser portion is approximately 0.6 to 0.7.
 19. The method ofclaim 17, wherein a degree of divergence of the separator portion isapproximately 0.3 to 0.4.
 20. The method of claim 1, wherein thesubstrate is a silicon wafer.